(K-4)(K+9)=14

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Solution for (K-4)(K+9)=14 equation: 


Simplifying
(K + -4)(K + 9) = 14

Reorder the terms:
(-4 + K)(K + 9) = 14

Reorder the terms:
(-4 + K)(9 + K) = 14

Multiply (-4 + K) * (9 + K)
(-4(9 + K) + K(9 + K)) = 14
((9 * -4 + K * -4) + K(9 + K)) = 14
((-36 + -4K) + K(9 + K)) = 14
(-36 + -4K + (9 * K + K * K)) = 14
(-36 + -4K + (9K + K2)) = 14

Combine like terms: -4K + 9K = 5K
(-36 + 5K + K2) = 14

Solving
-36 + 5K + K2 = 14

Solving for variable 'K'.

Reorder the terms:
-36 + -14 + 5K + K2 = 14 + -14

Combine like terms: -36 + -14 = -50
-50 + 5K + K2 = 14 + -14

Combine like terms: 14 + -14 = 0
-50 + 5K + K2 = 0

Factor a trinomial.
(-10 + -1K)(5 + -1K) = 0


Subproblem 1
Set the factor '(-10 + -1K)' equal to zero and attempt to solve:

Simplifying
-10 + -1K = 0

Solving
-10 + -1K = 0

Move all terms containing K to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + -1K = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1K = 0 + 10
-1K = 0 + 10

Combine like terms: 0 + 10 = 10
-1K = 10

Divide each side by '-1'.
K = -10

Simplifying
K = -10

Subproblem 2
Set the factor '(5 + -1K)' equal to zero and attempt to solve:

Simplifying
5 + -1K = 0

Solving
5 + -1K = 0

Move all terms containing K to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1K = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1K = 0 + -5
-1K = 0 + -5

Combine like terms: 0 + -5 = -5
-1K = -5

Divide each side by '-1'.
K = 5

Simplifying
K = 5
Solution
K = {-10, 5}

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